How do you convert $0.bar(15)$ (15 being repeated) to a fraction?

Question

27401 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-18T03:50:13

$5/33$

We first let $0.bar(15)$ (15 being repeated) be $x$ .

Since $x$ has $2$ decimal places recurring, we multiply it by $100.$

$" "x = 0.151515....$
$100x = 15.151515...$

Next, we subtract them.

$100x - x = 15.151515 - 0.151515$

$99x = 15$

Lastly, we divide both sides by $99$ to get $x$ as a fraction.

$x = 15/99$

$= 5/33$

How do you convert 0.bar(15)0.bar(15) (15 being repeated) to a fraction?